Hilary Putnam suggests that the essence of the realist conception of mathematics is that the statements of mathematics are objective so that the true ones are objectively true. An argument for mathematical realism, thus conceived, is implicit in Putnam's writing. The first premise is that within currently accepted science there are objective truths. Next is the premise that some of these statements logically imply statements of pure mathematics. The conclusion drawn is that some statements of pure mathematics are objectively true. A key principle assumed is that if one statement logically implies a second, then if the first is objectively true so is the second. A question about this principle is raised and answered. The problem with the argument is with the second premise.